Prediction of necking instability under tension-shear stress state based on updated modified maximum force criterion

Abstract

During the process from sheet forming to failure, the material might undergo uniform deformation, diffused necking (DN), localized necking (LN), and finally ductile fracture (DF). Researchers have found that a competitive mechanism exists between the LN-induced failure mode and DF-induced failure mode in the ductile metallic material. For tension shear (TS) stress state, most studies are focused on the DF prediction. This paper is concerned with necking instability in TS region and the prediction of necking failures. An updated modified maximum force criterion (uMMFC) model is proposed by considering the effect of in-plane shear stress, in which the strain path at LN onset under TS is no longer plane strain tension but varies with the initial path. Meanwhile, the effect of through-thickness normal stress is introduced into the uMMFC model. By comparing the forming limits obtained from the uMMFC, the original MMFC and the experimental results under uniaxial tension tests and Nakajima tests, it is concluded that the uMMFC model can well predict the forming limit curve under TS. Furthermore, the uMMFC model with the introduction of strain path modification after DN demonstrates a further improvement in prediction accuracy.